Question

Simplify:

\[7\frac{1}{3} \div \frac{2}{3}\text{ of }2\frac{1}{5} + 1\frac{3}{8} \div 2\frac{3}{4} - 1\frac{1}{2}\]

Answer 1

The given expression

\[= 7\frac{1}{3} \div \frac{2}{3}\text{ of }2\frac{1}{5} + 1\frac{3}{8} \div 2\frac{3}{4} - 1\frac{1}{2}\]
\[ = \frac{22}{3} \div \frac{2}{3}\text{ of }\frac{11}{5} + \frac{11}{8} \div \frac{11}{4} - \frac{3}{2} \]
\[ = \frac{22}{3} \div \frac{2}{3} \times \frac{11}{5} + \frac{11}{8} \div \frac{11}{4} - \frac{3}{2} \left( \text{Removing 'of '} \right)\]
\[ = \frac{22}{3} \div \frac{22}{15} + \frac{11}{8} \div \frac{11}{4} - \frac{3}{2} \]
\[ = \frac{22}{3} \times \frac{15}{22} + \frac{11}{8} \div \frac{11}{4} - \frac{3}{2} \left( \text{Removing }' \div ' \right)\]
\[ = 5 + \frac{11}{8} \times \frac{4}{11} - \frac{3}{2} \left( \text{Removing }' \div ' \right)\]
\[ = 5 + \frac{1}{2} - \frac{3}{2} (\text{ On simplifying})\]
\[ = \frac{10 + 1 - 3}{2} = \frac{8}{2} = 4\]